Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures.

Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control.

This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Review:

"The monograph is an excellent up-to-date authoritative reference covering original results which are presented in a rigorous, unified framework with examples. . . . The book will be useful primarily to applied mathematicians, control theorists and engineers, and anyone dealing with Lyapunov stability and control of nonlinear interconnected dynamic systems."--Lubomir Bakule, Zentralblatt MATH

Endorsement:

"This solid book provides a unique perspective and detailed account of the theory and applications of vector Lyapunov functions. I am confident it will be well received by researchers and graduate students working in control theory and large-scale systems."--Mehran Mesbahi, University of Washington

"With admirable and sound scholarship, and great scientific maturity, this book gives a methodical development of vector Lyapunov functions and vector control Lyapunov functions for the design of distributed control systems. It is a welcome addition to the literature and develops a rigorous foundation for applications in an important emerging new area."--Frank L. Lewis, University of Texas, Arlington